Article ID: CBB257161891

Mathematical Incompleteness Results in First-Order Peano Arithmetic: A Revisionist View of the Early History (2022)

unapi

In the Handbook of Mathematical Logic, the Paris-Harrington variant of Ramsey's theorem is celebrated as the first result of a long ‘search’ for a purely mathematical incompleteness result in first-order Peano arithmetic. This paper questions the existence of any such search and the status of the Paris-Harrington result as the first mathematical incompleteness result. In fact, I argue that Gentzen gave the first such result, and that it was restated by Goodstein in a number-theoretic form.

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Authors & Contributors
Luciano, Erika
Orlova, Nadezda
Nobrega, Hugo
Kennedy, Juliette
Soloviev, Sergei
Viana, Petrucio
Journals
History and Philosophy of Logic
Transactions of the Charles S. Peirce Society
Revue d'Histoire des Mathématiques
HOPOS
Historia Mathematica
Almagest
Publishers
Cambridge University Press
Vittorio Klostermann
Princeton University Press
Leo S. Olschki
Kluwer Academic
Birkhäuser Basel
Concepts
Logic
Philosophy of mathematics
Mathematics
Philosophy
Incompleteness theorems
Number theory; number concept
People
Frege, Gottlob
Peano, Giuseppe
Gödel, Kurt
Russell, Bertrand Arthur William
Peirce, Charles Sanders
Hilbert, David
Time Periods
20th century, early
19th century
20th century
Places
Russia
Poland
North America
Italy
Germany
France
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